Finite Group Databasebeta

← #7677686

Subgroups — #7677686

Order 512.

4588 conjugacy classes of subgroups.

The subgroup lattice has 1417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59908C212yesmaximal, complemented
2#59876C212yesmaximal, complemented
3#59682C212yesmaximal, complemented
4#59585C212yesmaximal, complemented
5#59448C212yesmaximal, complemented
6#59447C212yesmaximal, complemented
7#59443C212yesmaximal, complemented
8#59427C212yesmaximal, complemented
9#44752C214yesmaximal, complemented
10#44728C214yesmaximal, complemented
11#44680C214yesmaximal, complemented
12#44638C214yesmaximal, complemented
13#39768C211yesmaximal, characteristic
14#39640C211yesmaximal, characteristic, complemented
15#39051C214yesmaximal, complemented
16#38983C212yesmaximal, complemented
17#37943C212yesmaximal, complemented
18#37755C212yesmaximal, complemented
19#36487C212yesmaximal, complemented
20#36177C211yesmaximal, characteristic, complemented
21#36117C211yesmaximal, characteristic
22#35460C214yesmaximal, complemented
23#35103C211yesmaximal, characteristic
24#35099C212yesmaximal, complemented
25#34972C212yesmaximal, complemented
26#34229C212yesmaximal, complemented
27#34219C212yesmaximal, complemented
28C2×#2356C211yesmaximal, characteristic, complemented
29C4×#544C211yesmaximal, characteristic, complemented
30C2×#544C2211yescharacteristic
31C2×#529C2212yes—
32C2×#529C2212yes—
33C22×C4×Q8C2211yescharacteristic
34#2857C2211yescharacteristic
35#2856C2211yescharacteristic
36#2855C2212yes—
37#2854C2212yes—
38#2853C2214yes—
39#2850C2212yes—
40#2808C2212yes—
41#2806C2212yes—
42#2805C2212yes—
43#2804C2212yes—
44#2795C2214yes—
45#2793C2214yes—
46#2788C2214yes—
47#2783C2214yes—
48#2783C2214yes—
49#2779C2214yes—
50#2776C2214yes—
51#2776C2214yes—
52#2775C2214yes—
53#2774C2214yes—
54#2772C2214yes—
55#2766C2214yes—
56#2765C2214yes—
57#2759C2214yes—
58#2757C2214yes—
59#2751C2214yes—
60#2745C2214yes—
61#2739C2214yes—
62#2731C2214yes—
63#2725C2214yes—
64#2719C2214yes—
65#2716C2214yes—
66#2646C2212yes—
67#2643C2214yes—
68#2639C2212yes—
69#2618C2212yes—
70#2618C2212yes—
71#2608C2214yes—
72#2606C2214yes—
73#2604C2214yes—
74#2604C2214yes—
75#2601C2214yes—
76#2601C2214yes—
77#2596C2214yes—
78#2596C2214yes—
79#2594C2214yes—
80#2592C2212yes—
81#2592C2212yes—
82#2592C2212yes—
83#2590C2214yes—
84#2589C2214yes—
85#2587C2214yes—
86#2578C2214yes—
87#2577C2214yes—
88#2576C2214yes—
89#2575C2214yes—
90#2573C2214yes—
91#2572C2214yes—
92#2571C2211yescharacteristic
93#2570C2214yes—
94#2570C2212yes—
95#2568C2212yes—
96#2568C2211yescharacteristic
97#2568C2212yes—
98#2566C2212yes—
99#2565C2212yes—
100#2565C2212yes—
101#2565C2212yes—
102#2552C2211yescharacteristic
103#2548C2211yescharacteristic
104#2547C2212yes—
105#2546C2212yes—
106#2545C2212yes—
107#2545C2212yes—
108#2545C2212yes—
109#2545C2212yes—
110#2544C2212yes—
111#2544C2212yes—
112#2533C2214yes—
113#2533C2214yes—
114#2533C2214yes—
115#2532C2214yes—
116#2532C2214yes—
117#2531C2214yes—
118#2530C2214yes—
119#2529C2214yes—
120#2528C2214yes—
121#2527C2214yes—
122#2526C2214yes—
123#2526C2214yes—
124#2525C2214yes—
125#2525C2214yes—
126#2524C2214yes—
127#2524C2214yes—
128#2523C2214yes—
129#2518C2214yes—
130#2518C2214yes—
131#2515C2214yes—
132#2515C2214yes—
133#2514C2212yes—
134#2514C2212yes—
135#2514C2214yes—
136#2514C2212yes—
137#2514C2212yes—
138#2513C2212yes—
139#2512C2212yes—
140#2511C2212yes—
141#2511C2212yes—
142#2511C2212yes—
143#2510C2214yes—
144#2510C2214yes—
145#2509C2212yes—
146#2505C2214yes—
147#2503C2212yes—
148#2501C2212yes—
149#2497C2214yes—
150#2495C2214yes—
151#2493C2214yes—
152#2493C2214yes—
153#2488C2214yes—
154#2479C2214yes—
155#2475C2214yes—
156#2460C2214yes—
157#2454C2212yes—
158#2450C2214yes—
159#2448C2212yes—
160#2447C2212yes—
161#2447C2212yes—
162#2446C2212yes—
163#2446C2214yes—
164#2446C2212yes—
165#2444C2214yes—
166#2439C2214yes—
167#2436C2212yes—
168#2434C2212yes—
169#2425C2214yes—
170#2419C2214yes—
171#2413C2214yes—
172#2413C2214yes—
173#2396C2214yes—
174#2396C2214yes—
175#2373C2214yes—
176#2373C2214yes—
177#2372C2214yes—
178#2371C2214yes—
179#2367C2212yes—
180#2366C2211yescharacteristic
181#2365C2211yescharacteristic
182#2361C2212yes—
183#2361C2212yes—
184#2360C2212yes—
185#2360C2212yes—
186#2359C2214yes—
187#2359C2214yes—
188#2357C2212yes—
189#2357C2212yes—
190#2356C2212yes—
191#2356C2212yes—
192#2356C2212yes—
193#2356C2212yes—
194#2356C2212yes—
195#2356C2212yes—
196#2356C2214yes—
197#2356C2214yes—
198#2356C2214yes—
199#2355C2212yes—
200#2355C2212yes—
201#2355C2211yescharacteristic
202#2354C2212yes—
203#2353C2214yes—
204#2351C2212yes—
205Q8×C4⋊C4C2211yescharacteristic
206#2349C2212yes—
207#2346C2214yes—
208#2346C2214yes—
209#2343C2214yes—
210#2343C2214yes—
211#2334C2214yes—
212#2334C2214yes—
213#2331C2212yes—
214#2331C2212yes—
215#2330C2212yes—
216#2330C2212yes—
217#2329C2211yescharacteristic
218#2329C2212yes—
219#2329C2211yescharacteristic
220#2329C2212yes—
221#2325C2212yes—
222#2325C2212yes—
223#2325C2212yes—
224#2318C2214yes—
225#2318C2214yes—
226#2317C2212yes—
227#2316C2211yescharacteristic
228C4×C4⋊Q8C2212yes—
229C4×C4⋊Q8C2212yes—
230C4×C4⋊Q8C2212yes—
231C4×C4⋊Q8C2212yes—
232C4×#125C2212yes—
233C4×#125C2212yes—
234C4×#125C2212yes—
235C4×#125C2212yes—
236C4×#124C2212yes—
237C4×#124C2212yes—
238C4×#124C2212yes—
239C4×#124C2212yes—
240C4×C22⋊Q8C2211yescharacteristic
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2211yescharacteristic
243C4×#123C2214yes—
244C4×#123C2214yes—
245C4×#123C2214yes—
246C2×#391C2211yescharacteristic
247C2×#391C2211yescharacteristic
248C2×#387C2212yes—
249C2×#387C2212yes—
250#2283C2212yes—
251C2×#383C2212yes—
252C2×#382C2211yescharacteristic
253#2275C2214yes—
254C4×#117C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×#376C2212yes—
259C23×Q8C2311yescharacteristic
260#544—28no—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×#127C2311yescharacteristic
267#529—216no—
268#529—216no—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#124C2312yes—
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×C22⋊Q8C2311yescharacteristic
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2311yescharacteristic
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×C4×Q8—28no—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2314yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×#117C2312yes—
309C2×#117C2314yes—
310C2×#117C2314yes—
311C2×#117C2312yes—
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2311yescharacteristic
315C22×C4⋊C4C2311yescharacteristic
316C22×C4⋊C4C2311yescharacteristic
317C22×C4⋊C4C2311yescharacteristic
318C22×C42C2312yes—
319C22×C42C2312yes—
320C22×C42C2311yescharacteristic
321C22×C42C2312yes—
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324#401C2314yes—
325#401C2314yes—
326#401C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#399C2314yes—
348#399C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#395C2314yes—
385#395C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#391C2312yes—
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2314yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2314yes—
415#391C2312yes—
416#391C2311yescharacteristic
417#391C2311yescharacteristic
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#390C2312yes—
426#390C2312yes—
427#390C2312yes—
428#390C2312yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2314yes—
458#389C2312yes—
459#389C2311yescharacteristic
460#389C2311yescharacteristic
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2312yes—
511#387C2312yes—
512#387C2312yes—
513#387C2312yes—
514#387C2312yes—
515#387C2312yes—
516#387C2312yes—
517#387C2312yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2312yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2312yes—
579#385C2312yes—
580#385C2312yes—
581#385C2312yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#384C2312yes—
594#384C2312yes—
595#384C2312yes—
596#384C2312yes—
597#384C2311yescharacteristic
598#384C2311yescharacteristic
599#383C2314yes—
600#383C2314yes—
601#383C2314yes—
602#383C2314yes—
603#383C2314yes—
604#383C2314yes—
605#383C2314yes—
606#383C2314yes—
607#383C2314yes—
608#382C2312yes—
609#382C2312yes—
610#382C2312yes—
611#382C2312yes—
612#382C2312yes—
613#382C2312yes—
614#382C2312yes—
615#382C2314yes—
616#382C2314yes—
617#382C2312yes—
618#382C2312yes—
619#382C2314yes—
620#382C2314yes—
621#382C2314yes—
622#381C2314yes—
623#381C2314yes—
624#381C2314yes—
625#381C2314yes—
626#381C2314yes—
627#381C2314yes—
628#380C2311yescharacteristic
629#380C2311yescharacteristic
630#380C2312yes—
631#380C2314yes—
632#380C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2314yes—
636#380C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2311yescharacteristic
640C4×C4⋊C4C2311yescharacteristic
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695#376C2312yes—
696#376C2312yes—
697#376C2314yes—
698#376C2314yes—
699#376C2314yes—
700#376C2314yes—
701#376C2314yes—
702#376C2314yes—
703C2×#95C2312yes—
704C2×#95C2312yes—
705C2×#95C2311yescharacteristic
706C2×#95C2311yescharacteristic
707C2×#95C2312yes—
708C2×#95C2314yes—
709C2×#95C2312yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C43C2312yes—
715C43C2312yes—
716C22×Q8—24no—
717C22×Q8—42no—
718C22×Q8—42no—
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×D4C2414yes—
726C22×D4C2412yes—
727C22×D4C2412yes—
728C22×D4C2412yes—
729C23×C4C2412yes—
730C23×C4C2411yescharacteristic
731C23×C4C2411yescharacteristic
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2412yes—
737C23×C4C2411yescharacteristic
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C4⋊Q8—28no—
744C4⋊Q8—28no—
745C4⋊Q8—42no—
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748#127—42no—
749#126—216no—
750#126—216no—
751#125—28no—
752#125—28no—
753#125—28no—
754#125—28no—
755#124—28no—
756#124—28no—
757#124—44no—
758#124—44no—
759#124—44no—
760#123—216no—
761#123—216no—
762#123—48no—
763C22⋊Q8—28no—
764C22⋊Q8—24no—
765C22⋊Q8—28no—
766C22⋊Q8#4118yes—
767#121—28no—
768#121—28no—
769#121—44no—
770C4×Q8—28no—
771C4×Q8—216no—
772C4×Q8—28no—
773C4×Q8—28no—
774C4×Q8—28no—
775C4×Q8—44no—
776C4×Q8—42no—
777C4×Q8—42no—
778C4×Q8—44no—
779C4×Q8—44no—
780C4×D4—216no—
781C4×D4—28no—
782C4×D4—216no—
783C4×D4—28no—
784C4×D4—44no—
785C4×D4—44no—
786C4×D4—48no—
787#117—216no—
788#117—28no—
789#117—216no—
790#117—44no—
791C2×C4⋊C4—24no—
792C2×C4⋊C4—28no—
793C2×C4⋊C4—24no—
794C2×C4⋊C4—42no—
795C2×C4⋊C4—42no—
796C2×C4⋊C4—42no—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C42—28no—
892C2×C42—28no—
893C2×C42—42no—
894C2×C42—42no—
895C2×C42—44no—
896C2×C42#4118yes—
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2412yes—
931C2×C42C2412yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008C24C2514yes—
1009C24C2511yescharacteristic
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—24no—
1013C2×Q8—22no—
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—24no—
1017C2×Q8—24no—
1018C2×Q8—24no—
1019C2×Q8—41no—
1020C2×Q8—42no—
1021C2×Q8—42no—
1022C2×Q8—41no—
1023C2×Q8—41no—
1024C2×Q8—42no—
1025C2×Q8—42no—
1026C2×Q8—41no—
1027C2×Q8—416no—
1028C2×Q8C2×#4114yes—
1029C2×D4—28no—
1030C2×D4—28no—
1031C2×D4—28no—
1032C2×D4—24no—
1033C2×D4—24no—
1034C2×D4—24no—
1035C2×D4—24no—
1036C2×D4—42no—
1037C2×D4—42no—
1038C2×D4—42no—
1039C2×D4—42no—
1040C2×D4—42no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—22no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—22no—
1052C22×C4—24no—
1053C22×C4—22no—
1054C22×C4—28no—
1055C22×C4—28no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—41no—
1060C22×C4—41no—
1061C22×C4—41no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—42no—
1073C22×C4—42no—
1074C22×C4—41no—
1075C22×C4—41no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4C2×#4114yes—
1080C22×C4C2×#4114yes—
1081C22×C4C2×#4114yes—
1082C22×C4C2×#4114yes—
1083C22×C4C2512yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2511yescharacteristic
1110C4⋊C4—24no—
1111C4⋊C4—22no—
1112C4⋊C4—22no—
1113C4⋊C4—28no—
1114C4⋊C4—28no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—22no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—22no—
1135C4⋊C4—24no—
1136C4⋊C4—22no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—41no—
1156C4⋊C4—41no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4C2×#4118yes—
1174C4⋊C4C2×#4114yes—
1175C22⋊C4—24no—
1176C22⋊C4—28no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4C2×#4118yes—
1204C42—24no—
1205C42—24no—
1206C42—28no—
1207C42—28no—
1208C42—24no—
1209C42—24no—
1210C42—28no—
1211C42—28no—
1212C42—24no—
1213C42—24no—
1214C42—24no—
1215C42—22no—
1216C42—22no—
1217C42—24no—
1218C42—24no—
1219C42—24no—
1220C42—24no—
1221C42—41no—
1222C42—41no—
1223C42—42no—
1224C42—44no—
1225C42—44no—
1226C42—42no—
1227C42—44no—
1228C42—42no—
1229C42—42no—
1230C42—42no—
1231C42—44no—
1232C42—42no—
1233C42—42no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42C2×#4118yes—
1238C42C2×#4118yes—
1239C23—21no—
1240C23—21no—
1241C23—21no—
1242C23—21no—
1243C23—24no—
1244C23—24no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—24no—
1249C23—24no—
1250C23C22×#4112yes—
1251C23C22×#4112yes—
1252C23#58512yes—
1253C23C2611yescharacteristic
1254Q8—44no—
1255Q8—48no—
1256Q8—48no—
1257Q8—48no—
1258Q8—82no—
1259Q8—84no—
1260D4—416no—
1261D4—48no—
1262D4—84no—
1263D4—162no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—28no—
1279C2×C4—28no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—21no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—44no—
1338C2×C4—44no—
1339C2×C4—44no—
1340C2×C4—48no—
1341C2×C4—48no—
1342C2×C4—88no—
1343C2×C4—88no—
1344C2×C4—82no—
1345C2×C4—84no—
1346C2×C4—82no—
1347C2×C4—84no—
1348C2×C4—164no—
1349C2×C4C22×#4114yes—
1350C2×C4C22×#4112yes—
1351C2×C4C22×#4112yes—
1352C2×C4C22×#4114yes—
1353C2×C4C22×#4114yes—
1354C2×C4C22×#4114yes—
1355C2×C4C22×#4112yes—
1356C2×C4C22×#4112yes—
1357C2×C4#58512yes—
1358C2×C4#58512yes—
1359C22—22no—
1360C22—22no—
1361C22—22no—
1362C22—22no—
1363C22—22no—
1364C22—22no—
1365C22—44no—
1366C22—44no—
1367C22—44no—
1368C22—44no—
1369C22—44no—
1370C22—44no—
1371C22—44no—
1372C22#348014yes—
1373C22C23×#4111yescharacteristic
1374C22C23×#4111yescharacteristic
1375C22C2×#58511yescharacteristic
1376C22C2×#58511yescharacteristic
1377C22C2×#58511yescharacteristic
1378C222−1+611yescharacteristic
1379C222−1+611yescharacteristic
1380C4—22no—
1381C4—22no—
1382C4—24no—
1383C4—24no—
1384C4—22no—
1385C4—24no—
1386C4—24no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4—44no—
1393C4—44no—
1394C4—44no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—41no—
1399C4—41no—
1400C4—42no—
1401C4—44no—
1402C4—42no—
1403C4—42no—
1404C4—42no—
1405C4—44no—
1406C4#349314yes—
1407C2—24no—
1408C2—84no—
1409C2C2×#348011yescharacteristic
1410C2C2×#349311yescharacteristic
1411C2#6286011yescharacteristic
1412C2#6293411yescharacteristic
1413C2#6296411yescharacteristic
1414C2#6299111yescharacteristic
1415C2#6300911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59908C2semidirect
2. #59876C2semidirect
3. #59682C2semidirect
4. #59585C2semidirect
5. #59448C2semidirect
6. #59447C2semidirect
7. #59443C2semidirect
8. #59427C2semidirect
9. #44752C2semidirect
10. #44728C2semidirect
11. #44680C2semidirect
12. #44638C2semidirect
14. #39640C2semidirect
15. #39051C2semidirect
16. #38983C2semidirect
17. #37943C2semidirect
18. #37755C2semidirect
19. #36487C2semidirect
20. #36177C2semidirect
22. #35460C2semidirect
24. #35099C2semidirect
25. #34972C2semidirect
26. #34229C2semidirect
27. #34219C2semidirect
28. C2×#2356C2semidirect
29. C4×#544C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#599082
#598762
#596822
#595852
#594482
#594472
#594432
#594272
#447522
#447282
#446802
#446382
#397682
#396402
#390512
#389832
#379432
#377552
#364872
#361772
#361172
#354602
#351032
#350992
#349722
#342292
#342192
C2×#23562
C4×#5442